Mathematics
Grade 9
15 min
Surface area
Surface area
What you'll learn
- Identify the different two-dimensional shapes that make up the surface of a given three-dimensional object (cube, rectangular prism, triangular prism, and cylinder).
- Calculate the surface area of cubes and rectangular prisms by correctly applying the appropriate formulas and showing all steps in the calculation.
- Explain, in writing or verbally, how to determine the surface area of a three-dimensional object by summing the areas of its individual faces.
- Solve real-world problems involving surface area, such as calculating the amount of material needed to wrap a gift or paint a box, with 80% accuracy.
- Apply the concept of surface area to solve a real-world problem, such as calculating the amount of wrapping paper needed for a gift box, and justify the solution with clear mathematical reasoning.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define surface area and identify the components of 3D shapes (faces, bases, lateral area).
Calculate the surface area of right prisms and cylinders using the correct formulas.
Calculate the surface area of right pyramids and cones, including finding the slant height when necessary.
Calculate the surface area of a sphere.
Solve multi-step problems involving the surface area of composite 3D objects.
Algebraically rearrange surface area formulas to solve for an unknown dimension, such as radius or height.
Ever wondered how much wrapping paper you *actually* need for a gift, or how much paint to buy for your room? 🎁 That's all about surface area!
In this tutorial, we'll explore surface area, which is the total area of all the outside surfaces of a...
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Key Concepts & Vocabulary
TermDefinitionExample
Surface Area (SA)The sum of the areas of all the faces or surfaces of a three-dimensional object. It is measured in square units (e.g., cm², m²).The surface area of a cube with 2 cm sides is the sum of the areas of its 6 square faces: 6 * (2 cm * 2 cm) = 24 cm².
NetA two-dimensional pattern that can be folded to create a three-dimensional shape.A T-shape made of six squares is a net for a cube. Calculating the area of the net gives you the surface area of the cube.
Lateral AreaThe surface area of a 3D object, excluding the area of its base(s).For a can of soup, the lateral area is the paper label that wraps around the can, not including the top and bottom metal circles.
BaseThe face of a 3D object from which its height is measured. Prisms and cylinders have two paral...
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Core Formulas
Surface Area of a Right Cylinder
SA = 2πr² + 2πrh
Use this for any right cylinder, like a can or a pipe. '2πr²' is the area of the two circular bases, and '2πrh' is the lateral area (the rectangle that wraps around).
Surface Area of a Right Cone
SA = πr² + πrl
Use this for any right cone. 'πr²' is the area of the circular base, and 'πrl' is the lateral area. 'l' is the slant height, not the perpendicular height.
Surface Area of a Sphere
SA = 4πr²
Use this for any sphere, like a ball or a globe. This formula calculates the entire outer surface area.
Surface Area of a Right Pyramid
SA = (Area of Base) + (Area of all triangular faces)
This is a general rule. For a square-based pyramid, it becomes SA = s² + 2sl, w...
5 more steps in this tutorial
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Challenging
A toy rocket is formed by a cone on top of a cylinder. The cylinder has a radius of 3 cm and a height of 10 cm. The cone has the same radius and a slant height of 5 cm. What is the total surface area of the toy?
A.84π cm²
B.93π cm²
C.75π cm²
D.102π cm²
Challenging
A cylinder has a height of 5 cm and a total surface area of 48π cm². What is its radius?
A.3 cm
B.4 cm
C.6 cm
D.8 cm
Challenging
A right pyramid has a rectangular base measuring 12 cm by 16 cm. Its perpendicular height is 15 cm. Calculate its total surface area.
A.720 cm²
B.564 cm²
C.648 cm²
D.768 cm²
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Frequently asked questions
What grade level is "Surface area"?
Surface area is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Surface area?
You'll be able to: Identify the different two-dimensional shapes that make up the surface of a given three-dimensional object (cube, rectangular prism, triangular prism, and cylinder); Calculate the surface area of cubes and rectangular prisms by….
Is "Surface area" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Surface area?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.